TABLE OF CONTENTS Even the most reclusive theoretician is aware of the fact that the brain is not just a single cell that it is a complex network of neurons with interconnections. However, for simplicity, we have so far tried to understand the development of neural properties primarily from the properties of single cells, ignoring most of the possible contributions of lateral connectivity and feedback. In Chapter 4 we did explore a mean-field approximation for network interactions, and in Section 4.3 we explored the effect of the lateral interactions, using a matrix analysis. We summarize the main results of these chapters below:
Network interactions can
change the single-cell receptive field properties
change the organization of receptive fields across the network
The mean-field approximation addresses (1) above, by allowing the effective weights from all-excitatory feed-forward connections to be both positive and negative. In this way, the lateral interaction allows the development of single-cell receptive fields which would not be possible without the lateral connectivity. The mean-field does not address (2) above, because it ignores possible correlations between output neuron responses.
The matrix analysis assumes bi-polar weights or, in other words, weights that can be either positive or negative. The conclusions relate both to (1) and (2) above. The main conclusions of this analysis are
the lateral connectivity does not change the number of fixed points or their stability
the lateral connectivity does not change the values of the fixed points, for the outputs of the neurons.
